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A theoretical approach for a non-perturbative dynamical description of twointeracting atoms in an optical lattice potential is introduced. The approachbuilds upon the stationary eigenstates found by a procedure described inGrishkevich et al. [Phys. Rev. A 84, 062710 (2011)]. It allows presently totreat any time-dependent external perturbation of the lattice potential up toquadratic order. Example calculations of the experimentally relevant cases ofan acceleration of the lattice and the turning-on of an additional harmonicconfinement are presented.

Non-perturbative theoretical description of two atoms in an optical lattice with time-dependent perturbations